Using logarithms to do square root seems silly. Successive approximation methods are pretty efficient, even with a bad first guess.

BTW: The MoMad coefficients for the sin function look like a Chebychev approximation to a truncated standard sin series.

For general purpose usage, mathematical functions are expected to handle almost any range of arguments. The basic routines lose speed and compactness due to being able to cope with a wide range of arguments.

The MoMad approximation to the sin function would provide hardly any precision if given an angle like 150 degrees. An exponential function which can handle e^50 has some work to do.